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| Chaos Control and Behavior Analysis of a Discrete-Time Dynamical System with Competitive Effect |
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| KeyWord:Predator-prey system, flip bifurcation, Neimark-Sacker bifurcation, competitive effect, chaos |
| Author Name | Affiliation | | Xiongxiong Du | Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China | | Xiaoling Han | Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China | | Ceyu Lei | Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China |
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| Abstract: |
| This paper is about a class of discrete-time dynamical systems with competitive effects. The local stability of the positive equilibrium point of the system and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are discussed by using the center manifold theorem and bifurcation theory. In addition, the direction of the flip bifurcation and Neimark-Sacker bifurcation is given. Furthermore, a feedback control strategy is employed to control bifurcation and chaos in the system. Finally, flip bifurcation, Neimark-Sacker bifurcation and chaos control strategy are verified with the help of numerical simulations. |
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